The recent detection of gravitational waves enables new opportunities to investigate the fundamental laws of nature. Gravitational wave astrophysics represents an exciting new tool, but truly revolutionary progress requires the combination of different data sets. Co-analyzing observations from different messengers and experiments will be more powerful than the simple addition of catalogs, enabling new tests that will otherwise not be possible; therefore, combined data sets will set up the future state-of-the-art of cosmological studies. I will present a few such possibilities recently proposed, focusing in particular on investigating the physics acting in the early universe, the nature of dark matter and models of gravity.